The double of a hyperbolic manifold and non-positively curved exotic 𝑃𝐿 structures

Ontaneda, Pedro

doi:10.1090/S0002-9947-02-03076-3

The double of a hyperbolic manifold and non-positively curved exotic $PL$ structures
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Trans. Amer. Math. Soc. 355 (2003), 935-965 Request permission

Abstract:

We give examples of non-compact finite volume real hyperbolic manifolds of dimension greater than five, such that their doubles admit at least three non-equivalent smoothable $PL$ structures, two of which admit a Riemannian metric of non-positive curvature while the third does not. We also prove that the doubles of non-compact finite volume real hyperbolic manifolds of dimension greater than four are differentiably rigid.

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